Synthetic Dry Adhesives

ABSTRACT

A method of forming synthetic dry adhesives is provided that includes using a wedge-shaped tool to form mold cavities in a mold, filling the mold cavities with an elastomeric adhesive, removing the elastomeric adhesive from the mold, where a tapered lamellar ridge extends from a surface of the elastomeric adhesive, treating a tip of the extending ridge with a film of uncured elastomeric material, and curing the film of uncured material while the extending ridge is pressed against a substrate surface having a smoothness or texture. The synthetic dry adhesive comprises a close-packed array of tapered lamellar ridges, where the centerline of a ridge is angled relative to a direction normal to the synthetic dry adhesive and the cross section includes an internal taper. The tapered ridge bends when it contacts a surface, whereupon the radius of curvature of the ridge increases monotonically with increasing shear load.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional PatentApplication 61/517,496 filed Apr. 20, 2011, which is incorporated hereinby reference.

STATEMENT OF GOVERNMENT SPONSORED SUPPORT

This invention was made with Government support under contract NIRT0708367 awarded by National Science Foundation (NSF), and under contract1118729-2-TFLAP awarded by DARPA. The Government has certain rights inthis invention.

FIELD OF THE INVENTION

This invention relates to synthetic dry adhesives and methods of makingthereof.

BACKGROUND OF THE INVENTION

Impressive advancements have been made in the field of gecko-inspiredsynthetic dry adhesives. A large range of manufacturing methods forthese adhesives has been reported in the literature. However, the use ofsuch adhesives in applications such as climbing has been much morelimited, with just a few examples reported. It has generally been foundthat the adhesion levels generated in real-world climbing applicationsare significantly lower than those obtained using small samples inbench-top experiments.

One reason for this disparity is that, in addition to conforming tosurfaces and generating useful levels of adhesion, the adhesives haveadditional requirements when used for climbing. The first of theserequirements is controllability, i.e., the adhesives should not besticky in the default state and adhere only when it is desirable. In anyother case, energy will be wasted as it is expended in attaching anddetaching the adhesive for each step. Controllability can be achieved byusing switchable structures or by creating directional adhesive featureswhose adhesion generation is a function of applied shear load.

The second requirement is durability. The adhesives must undergothousands of attach/detach cycles without significant loss of adhesiveproperties and, ideally, should resist fouling and be easy to clean.Durability is also correlated with controllability: gentle attach/detachcycles reduce mechanical wear and promote long life.

Micro-wedges are an example of a synthetic dry adhesive that has beensuccessfully applied to climbing robots. Micro-wedges are simple,controllable, and durable structures that have enabled robots weighing 1kg and more to climb on glass, plastic, wood paneling, painted metal,and similar surfaces. When unloaded, as shown in an oblique perspectiveview in FIG. 1 a, they present a very small real area of contact with asurface and generate negligible adhesion. However, when loaded in apreferred shear direction, as shown in FIG. 1 b, they bend, creating alarger contact area and generating adhesion that is proportional to theshear load. The micro-wedges' asymmetric taper ensures that the radiusof curvature of the feature at the proximal edge of the contact patchincreases with increasing shear load, allowing the tapered features tooutperform features of constant cross-section at high shear loads.Furthermore, they may be easily cleaned using a piece of sticky tape.

In previous work, micro-wedges were manufactured by casting apolydimethylsiloxane (PDMS) silicone elastomer into molds createdthrough a photolithographic process in which SU-8® photoresist(MicroChem Corp.) was subjected to two exposures, one angled, onevertical, through contact masks. The necessity of a thick photo-resistlayer combined with the requirement for high precision alignment ofexposures resulted in a time consuming, expensive mold fabricationprocess with relatively low yield.

What is needed is a method of fabricating controllable and durablesynthetic dry adhesives that does not use an expensive photolithographicprocess, and which provides synthetic dry adhesives with performance inclimbing and other applications that is comparable to or better than themicro-wedges used in previous work.

SUMMARY OF THE INVENTION

To address the needs in the art, a method of forming synthetic dryadhesives is provided, which according to one embodiment includes usinga wedge-shaped tool to form mold cavities in a mold, where the moldcavities comprise a depth t and a spacing h, filling the mold cavitieswith an elastomeric adhesive, removing the elastomeric adhesive from themold, where a tapered lamellar ridge extends from a surface of theelastomeric adhesive, treating a tip of the extending tapered lamellarridge with a film of uncured elastomeric material, and curing the filmof uncured material while the extending tapered lamellar ridge ispressed against a substrate surface.

According to one aspect of the invention, the mold includes ahomogeneous wax composition having a Young's modulus to yield stressratio E/Y greater than 100.

In another aspect of the invention, the wedge-shaped tool comprises atleast a primary bevel, or includes a primary bevel, a secondary beveland a tertiary bevel. In one aspect the wedge-shaped tool includes alubricated surface.

According to one aspect of the invention, the wedge-shaped tool is movedalong a 2-dimensional or 3-dimensional trajectory into the mold until atip of the wedge-shaped tool reaches the depth t below a top surface ofthe mold.

In a further aspect of the invention, a trajectory of the tool iscontrolled to move displaced mold material in a desired direction, wherethe mold cavities are desirably spaced and a shape of the cavities iscontrolled.

In yet another aspect of the invention, a centerline of the wedge-shapedtool is set at an angle λ with respect to a top surface of the mold,where a trajectory of the tool is at an intermediate angle θ withrespect to a top surface of the mold, where the angle θ is in a range of0<θ<λ.

According to another aspect of the invention, the elastomeric adhesiveis an elastomer that can include silicones, polyurethanes, orpolypropylene.

In a further aspect of the invention, a tip of the extending taperedlamellar ridge is treated with a film of uncured elastomeric material,where the uncured elastomeric material is disposed on one or both sidesof the lamellar ridge.

According to another aspect of the invention, the substrate surfaceincludes a smooth or textured surface, where the surface is disposed totransfer a desired smoothness or desired texture to a film of theuncured elastomeric material as the uncured elastomeric material cures.

In a further aspect of the invention, a siping step is used when theadhesive is de-molded, where the siping step includes a cutperpendicular to the tapered lamellar ridge at a desired frequency toimprove adhesion on textured surfaces having micro-scale roughness,where independent adhesive sections of the extending tapered lamellarridge conform to the textured surface.

According to another embodiment, a synthetic dry adhesive is providedthat includes a close-packed array of elastomeric adhesive wedge-shapedlamellar ridges where a cross-section of the close-packed array includesa base of a leading edge of one lamellar ridge contacting a base of atrailing edge of an adjacent lamellar ridge, where the lamellar ridgecomprises an internal taper spanning from a base of the lamellar ridgeto a pointed tip of the lamellar ridge, where a centerline of thelamellar ridge is angled relative to a direction normal to the syntheticdry adhesive, and a secondary elastomeric adhesive layer disposed on oneor both sides of the tip of the wedge-shaped lamellar ridge, where thesecondary layer comprises a textured or flat surface.

According to one aspect of the current embodiment, the wedge-shapedlamellar ridge bends into a curve when it contacts a surface, whereuponthe radius of curvature of the wedge-shaped lamellar ridge increasesmonotonically with increasing shear load.

In another aspect of the current embodiment, the tip-to-tip spacing hbetween adjacent lamellar ridges is as low as 6 μm.

In a further aspect of the current embodiment, the angle of thecenterline of the tapered ridge is up to 50 degrees relative to thenormal direction.

In one aspect of the current embodiment, both sides of the tapered ridgeare angled relative to the normal direction.

According to another aspect of the current embodiment, the elastomericadhesive is an elastomer that includes silicones, polyurethanes, andpolypropylene.

In yet another aspect of the current embodiment, the tip of thewedge-shaped lamellar ridge includes a film of cured elastomericmaterial having a desired smoothness or texture on one or both sides ofthe wedge-shaped lamellar ridge.

According to a further aspect of the current embodiment, the lamellarridge includes siping, where the siping is disposed across thewedge-shaped lamellar ridge.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 a-1 b show prior art SEM micrographs of PDMS directionaladhesive features: (a) perspective view of unloaded micro-wedges from aphotolithographic mold, (b) planar view of micro-wedges under shearloading

FIG. 2 a-2 c show cross-section views of wedge-shaped lamellar ridgeshaving cured elastomeric material with a desired smoothness or textureon one or both sides of the wedge-shaped lamellar ridge, according tosome embodiments of the current invention.

FIG. 3 a-3 b show diagrams of the geometry and the parameters of themicro-machining process for a single cavity, where “Traj.” is the tooltrajectory; “S.P.” is the shear plane, according to one embodiment ofthe invention.

FIG. 4 a-4 e show a diagram of the steps for treating the tips of theextending tapered lamellar ridges with a film of elastomeric material,according to one embodiment of the invention.

FIG. 5 a-5 b show perspective drawings of post-treated wedge-shapedlamellar ridges before and after a siping step, according to oneembodiment of the invention.

FIG. 6 show cross-section views of a microtome blade having threedifferent beveled sections the wedge-shaped tool bevels, according toone embodiment of the invention.

FIG. 7 a-7 b a micrograph of a single mold cavity created in cuttingforce tests showing triangular built-up region, and measured shearstress with values of shear yield stress k for comparison (T, S, and Ccorrespond to trajectories parallel to the tertiary bevel, secondarybevel, and centerline of the tool), according to one embodiment of theinvention.

FIGS. 8 a-8 d show micrographs of the effect of trajectory angle on moldcavity shape. For some trajectories (a-b), a continuous chip of built-upmaterial is formed after the final cavity, according to one embodimentof the invention.

FIG. 9 shows geometric data taken from characterization experimentmicrographs (FIGS. 8 a-8 d), according to one embodiment of theinvention.

FIG. 10 shows a graph of a comparison of the limit curves formacroscopic arrays of adhesive features produced with micro-machinedmolds and photolithographic molds, according to one embodiment of theinvention.

DETAILED DESCRIPTION

Directional dry adhesives are inspired by animals such as geckos and area particularly useful technology for climbing applications. Previously,they have generally been manufactured using photolithographic processes.The current invention provides a micro-machining process that makes cutsin a soft material using a sharp, lubricated tool to create closelyspaced negative cavities of a desired shape. The machined materialbecomes a mold into which an elastomer is cast to create the directionaladhesive. The trajectory of the tool is varied to avoid plastic flow ofthe mold material that may adversely affect adjacent cavities. Therelationship between tool trajectory and resulting cavity shape isestablished through modeling and process characterization experiments.

The micro-machining process of the current invention is much lessexpensive than previous photolithographic processes used to createsimilar features and allows greater flexibility with respect to themicro-scale feature geometry, mold size, and mold material. Themicro-machining process produces controllable, directional adhesives,where the normal adhesion increases with shear loading in a preferreddirection. This is verified by multi-axis force testing on a flat glasssubstrate. Upon application of a post-treatment to improve thesmoothness of the engaging surfaces of the features after casting, theadhesives significantly outperform comparable directional adhesives madefrom a photolithographic mold.

One embodiment of the current invention includes a mold created with amicro-machining process that involves making a pattern of cavities in amold using a narrow cutting tool. Machining processes have been usedpreviously to create stamps for soft lithography and synthetic adhesivestructures using nano-indenters and AFM tips, but neither fabricationnor testing of macroscopic adhesive arrays (˜1 cm²) has beendemonstrated, the aspect ratio of the resulting features has been low,and the features have not been closely spaced. This in turn leads tounused space between features, decreased real area of contact, anddecreased adhesive performance.

The current invention provides a micro-machining process that is ahybrid of orthogonal machining and wedge indenting. According to oneembodiment, a sharp wedge-shaped tool is moved along an obliquetrajectory into a soft mold surface, producing wedge-shaped cavities ofdepth on the order of up to 500 μm and of any desired width, forexample. By controlling the tool geometry and trajectory and repeatingthis operation in a pattern across the mold surface, it is possible toobtain a dense packing of sharp, wedge-shaped cavities. As an example,casting PDMS into these cavities produces micro-wedge lamellar featuresas seen in FIG. 5 a. In comparison to photolithography, the methodpresented here is cheaper, faster, and affords greater freedom tocontrol the cavity geometry, which governs adhesive performance.

The main motivation of the current invention is the need for a practicaladhesive for climbing. The new micro-machined features, upon applicationof a post-treatment process according to another embodiment (see FIGS. 2a-2 c and FIGS. 4 a-4 e), perform significantly better thanphotolithographic micro-wedges in adhesive tests, where thepost-treatment process includes treating a tip of the extending taperedfeatures with a film of uncured elastomeric material disposed on one orboth sides of the features, and a treatment transfer substrate isdisposed to transfer a desired smoothness or desired texture to theuncured film as it cures. The improvement is partly a result of havinggreater freedom to control the wedge taper and angle of inclination.Arrays of the new features have been produced and tested, with maximumnormal adhesion of 38 kPa attained at a shear stress of 49 kPa for anarray of area 1.21 cm².

In addition, the micro-machined features formed by the method of thecurrent invention retain the controllability and durability ofphotolithographic micro-wedges.

In order to better understand the mechanics involved, a micro-machiningprocess may be described using numerical finite-element modeling orsemi-analytic theoretical models. Theoretical models are mostly appliedto ideal rigid-plastic materials and are not as likely to accuratelypredict the forces and deformations. Conversely, state of the artnumerical models can account for realistic material behavior andfriction effects. However, the material properties and tribologicalbehavior of the wax mold material used here have not been sufficientlywell characterized to justify a numerical model. Moreover, it is notrequired to produce a numerical prediction of the cutting forces interms of the cutting parameters (e.g. cutting depth, speed, friction,tool angle, or tip radius) as the forces are, in any case, quite low.

Instead, it is useful to understand how the cutting parameters and toolgeometry affect the deformation behavior. In particular, it is desirableto produce a tightly packed array of cavities in order to obtain a highdensity of adhesive features. Accordingly, an important question iswhether displaced material is moved mainly in the forward direction(towards the unmachined part of the mold) or the rearward (tending toclose up the previously made cavity). Semi-analytic theoretical modelscan provide this insight without recourse to running numeroussimulations, which may be poorly convergent or sensitive to boundaryconditions and may require frequent re-meshing due to the largedeformations involved.

If the cutting depth t and the tool cross-section are constant along thewidth of the cavity (into or out of the page in FIGS. 3 a-3 b), and if tis much smaller than the width of the cavity, then the stressed materialis confined to a long, narrow prismatic region. In the experimentsdescribed here, t≦100 μm and the cavity width is greater than 10 mm, soit is reasonable to assume that the material is in a state of planestrain.

The process bears resemblance to two classical problems fromplane-strain plasticity theory: oblique wedge indenting, in which arigid wedge-shaped tool penetrates the work surface, and orthogonalmachining, in which the tool removes a thin strip of material by movingparallel to the work surface. The process according to the currentinvention is a generalization of the two processes: the tool iswedge-shaped with internal angle 2β, the centerline of the tool is setat an angle λ with respect to the work surface, and the direction ofmotion of the tool is neither parallel to the centerline (as in wedgeindenting) nor to the work surface (as in orthogonal machining), butinstead is set at an intermediate angle 0<θ<λ, as shown in FIGS. 3 a-3b.

To model this process analytically, it is assumed that the work materialis perfectly rigid-plastic. While most plasticity studies have beenconcerned with the plastic behavior of metals, wax has also been used asa work material, and waxes can be closer to rigid-plastic than metals.The wax used in this example has been found through axial compressiontesting to have a low shear yield strength (approximately 2 MPa) andlittle work hardening; however, it does exhibit some elastic recovery,which can affect the forces and cavity geometry during micro-machining.

Given these assumptions, it is feasible to adapt an existingsemi-analytic model to the present situation to obtain an estimate ofthe flow of material on both sides of the tool and the expected buildupregion adjacent to the cavity.

For a perfect rigid-plastic material, the interior shape of the cavitywill be identical to the swept volume of the tool as it moves along itstrajectory, which means that any trajectory angle θ can be chosen fromthe range λ−β<θ<λ+β without affecting the shape of the cavity. However,the extent of plastic deformation and the amount of buildup occurring onthe leading and trailing faces of the tool will vary with θ. If materialis displaced on both sides of the tool, and the mold cavities are spacedclosely, this flow will result in partial collapse of the previouslyformed cavity.

In order to minimize this effect, the trajectory angle may instead bechosen to lie outside this range: θ=λ−β−ε, where ε>0 is a relief angle.This increases the angular width of the cavities by the angle ε. Thisgeometry can be seen in FIGS. 3 a-3 b. The benefit of the relief angleis that the trailing side of the tool should no longer make contact withthe wall of the cavity. As a result, assuming that the tip of the toolis sufficiently sharp, the zone of plastic deformation is limited to theleading side of the tool only, and material on the trailing side remainsrigid throughout the process, theoretically preventing partial collapseof the previous cavity. In one aspect of the invention, the angle of thecenterline of the resulting adhesive feature produced by this process isup to 50 degrees relative to the normal direction.

Two possibilities are predicted for the plastic deformation on theleading side of the tool.

In the first case, the plastic region covers the entire area ofdisplaced material, and it is possible to construct a slip-line fieldthroughout this region. In the second case, the plastic region isrestricted to a single shear plane, and elsewhere the material is rigid.

This second case occurs if the trajectory angle is lower than a criticalvalue:

2 tan θ<+[1+tan(α+θ)]²  (1)

However, this equation is always satisfied if the rake angle α ispositive, as in the present case. Therefore, the model predicts that asingle shear plane solution is appropriate on the leading face of thetool. The model also provides a prediction of the shear plane angle φbased on an energy-minimization argument, but since the model does notinclude friction this prediction is not expected to be accurate.Furthermore, there is doubt about the theoretical and experimentalvalidity of this argument.

Despite the lack of a trustworthy prediction of the shear plane angle φ,the model can be used to make a testable prediction about the cuttingforces if φ can be measured experimentally. Let the net force applied bythe machine to the tool be denoted by

F=F _(x) {circumflex over (x)}+F _(y) ŷ  (2)

and let the total force on the shear plane be denoted by

f=f _(s) ŝ+f _(n) {circumflex over (n)}  (3)

as shown in FIGS. 3 a-3 b. In accordance with the model, it is assumedthat the displaced material is limited to a triangular built-up regionalso shown in FIGS. 3 a-3 b. As long as there is no contact on thetrailing side of the tool, these forces are equal: F=f, and therefore:

f _(s) =F _(x)({circumflex over (x)}·ŝ)+F _(y)(ŷ·ŝ)=F _(x) cos φ+F _(y)sin φ  (4)

This relationship does not require any assumptions about the shear planeangle φ or the friction at the leading side of the tool. Finally,according to the theory of perfect rigid-plastic materials in planestrain, the shear stress along the shear plane is constant and equal tothe shear yield stress k:

f _(s) /A=k  (5)

where A is the area of the shear plane.

Although the semi-analytic model cannot be expected to produce acomplete prediction of the cutting forces with high accuracy, itproduces a useful prediction about the deformation mode of the material(the existence of a shear plane), and it is also useful forunderstanding relationships among λ, β, θ, and φ. This leads to theexpectation that most of the displaced material will be pushed forwardif the trajectory angle, θ, is sufficiently small compared to the angleof the trailing face of the tool, λ−β. In this situation, the model doesproduce a testable prediction about the cutting forces (Eqs. 4 and 5).

The mold fabrication method of the current invention relies on a few keycomponents to be effective. Most important is the wedge-shaped tool,whose shape strongly influences the shape of the resulting moldcavities. The tool used in this example is a PTFE-coated steeldisposable microtome blade (Delaware Diamond Knives D554X). This toolhas a fine surface finish, with blade roughness on length scales <<1 μm,an internal angle of 2β≈24°, and an edge radius of less than 0.9 μm.

The material used for the mold must also be selected for desirableproperties. An ideal material for machining would have a homogeneouscomposition, a relatively low yield strength, and perfect rigid-plasticbehavior to minimize elastic recovery of the machined region.Rigid-plastic behavior is most likely to occur in micro-machiningprocesses of the current invention if the included angle of the tool isacute and the ratio of Young's modulus to yield stress E/Y is large.According to one aspect, the mold includes a material composition havinga Young's modulus to yield stress ratio E/Y greater than 100.

In one embodiment, a soft, rolled sheet wax (Kindt-Collins Master®Regular Sheet Wax) is used, having a ratio of Young's modulus to yieldstress of approximately E/Y≈110-160. For this value of E/Y with a toolangle of 24°, the deformation behavior is not dominated by elasticeffects and rigid-plastic behavior may be possible.

Adhesive wear at the tool-mold interface is undesirable and could leadto a poor surface finish. However, this is mitigated by lubricating theinterface, according to one embodiment. In addition a post-treatingprocess has been devised to refinish the surfaces entirely. For thesereasons the tribological properties of the mold material are not a majorconcern for material selection.

The micro-machining process according to one embodiment of theinvention, may be performed on a standard CNC milling machine or othermachine with positioning control in at least two axes and sufficientaccuracy. In the current example of the invention, adhesives have beenproduced using a tabletop CNC milling machine with 1 μm precision (LevilWL400), a larger CNC milling machine with 2.5 μm precision (Haas VF-0E),and a motorized stage with an estimated accuracy of ±1 μm (VelmexMAXY4009C-S4 and Newport GTS30V).

Ultimately, the dimensions of an adhesive patch are constrained only bythe width of the microtome blade and the length of the workspace of themachine. With the equipment described above, it is possible to make asingle uninterrupted patch of adhesive as large as 76 mm wide by 762 mmlong or longer.

First, the wax is melted and cast into a block to improve theconsistency of its plastic behavior and to obtain a desirable formfactor for fixturing, and then it is cooled to room temperature. Themold surface is milled and planed to ensure it is flat and parallel tothe machine ways. Next, the surface is cleaned and the micro-machiningtool is mounted to the machine head. The blade is fixed so that itscenterline is tilted by a constant angle of λ=60° with respect to thehorizontal surface of the wax (see FIGS. 3 a-3 b). The tip of the bladeis then aligned to the wax surface.

The tool is moved by the machine along a specified 2-D or 3-D trajectoryinto the wax until its tip reaches a desired depth t in the negativey-direction (see FIGS. 3 a-3 b). At this point the tool is retractedabove the surface and then advanced a set distance in the positivex-direction to create a space between cuts. The cycle then repeats.

The tool trajectory may be chosen from a large space of possible paths.Varying the trajectory provides freedom to control the completed cavityshape and the plastic flow of the mold material.

Without lubrication, adhesive wear occurs between the tool and the moldmaterial. SEM examination of the features cast from these moldsindicates significant surface roughness on critical areas such as theengaging faces that will ultimately generate adhesion. To address thisissue, a lubricant may be added to the process to inhibit materialtransfer from the wax mold to the tool. Several fluids were tested,including various mixtures of water and surfactants in the form ofliquid dish soaps. Surface roughness was measured by capturingstereoscopic SEM images and generating 3D topographical plots using theAlicona Imaging MeX software package. Average roughness data were takenacross line profiles over the engaging surfaces of the features. Thebest surface finish, corresponding to an RMS roughness of approximately39 nm, was obtained with a 10:2 concentration of Ajax liquid dish soap(Colgate-Palmolive) to water.

The completed mold is cleaned with solvents and water to remove alltraces of lubricant. A PDMS silicone elastomer (Dow Corning Sylgard®170) is vacuum de-gassed and poured into the mold. Other materials caninclude elastomers such as silicones, polyurethanes, or polypropylene.For samples for adhesion force testing, a 300 μm thick backing layer ofPDMS is desired. This can be achieved by spinning the mold at 160 RPMfor 30 seconds, or alternatively a two-part mold may be created byplacing a flat sheet of glass upon 300 μm supports, which rest on thewax mold surface. For climbing applications, the sheet of glass may bereplaced by a rigid tile made of glass fiber or aluminum. The tile istreated with a primer (Dow Corning PR-1200), which allows the PDMS tobond directly to the tile. In any case, the casting is then allowed tocure at room temperature for 24 hours (heat acceleration is alsopossible). Once removed from the mold, the elastomeric adhesive is readyfor use. The mold may become damaged as the castings are de-molded, inwhich case the mold may be resurfaced and micromachined again before itsnext use.

While the addition of lubrication to the micro-machining processimproves the surface finish of the molds and molded features, there isstill some remaining roughness that can affect the performance of theadhesives by reducing the real area of contact between the adhesive andthe substrate. In order to further reduce this roughness, apost-treatment is employed after casting. This treatment adds a thinsecondary layer of PDMS to the engaging faces of the molded features.This layer may be smooth or textured as desired. In the case of a smoothlayer, the treatment proceeds as follows (see FIGS. 4 a-4 e):

1. Uncured PDMS is diluted to a concentration of 10% toluene by volume.The diluted mixture is then poured onto a four-inch quartz wafer andspun at 8000 RPM for 60 seconds to obtain a uniform thin layer 3-5 μmthick.2. One half of the wafer is cleaned using isopropyl alcohol, and thewafer and a cast adhesive sample are secured to a three axis motorizedpositioning stage.3. The sample is brought into contact with the PDMS-coated half of thewafer. After applying a normal load so that the features are in contactwith the wafer over approximately one third of their length, thefeatures are taken out of contact, leaving a thin, wet layer of PDMS onthe tips of the features.4. After this “inking” procedure, the features are loaded against thecleaned half of the wafer and held there in order to flatten this thin,wet layer as it cures.5. The cured thin layer binds strongly to the previously cured features.The post-treatment results in smooth patches of PDMS on the engagingfaces of the features (see FIG. 5).

For a climbing adhesive, which has been cast directly to a rigid tile,the post-treatment may be done without the motorized positioning stage,by simply using an appropriately sized weight. In this variation of theprocess, the wafer is placed on a flat surface, the adhesive is placedon the wafer (with the back of the tile facing up), and the weight isplaced on the tile. The best post-treatment results have been obtainedusing weights such that the average pressure is approximately 7-8 kPa,but this depends on the shape and stiffness of the features.

Experiments were performed to test the semi-analytic model introducedabove, to empirically characterize the micro-machining process, and tomeasure the adhesive performance of macroscopic arrays of micro-machinedmicro-wedges. However, it is first necessary to look more closely at thegeometry of the microtome blades used here as micro-machining tools.

According to one aspect of the current embodiment, the wedge-shaped toolincludes a wedge, or at least a primary bevel. As seen in the embodimentshown in FIG. 6, the shape of the tool is not simply a primary bevel.Instead, the wedge-shaped tool is sharpened to a profile with threedifferent beveled sections. According to one embodiment, the primarybevel begins approximately 1.7 mm from the tip and has an angle of 12°(this section is above the wax mold at all times). The secondary bevelbegins 270 μm from the tip and has an angle of 24°, and the tertiarybevel extends over the final 40 μm of the blade's length and is 34°wide. The tip is too small to be seen at this magnification, but anupper limit radius of 0.9 μm may be established.

In the described machining geometry, the border between the secondaryand tertiary bevels is below the surface of the wax whenever the bladeis inserted more than 40 μm deep. However, the mold cavities created bythe micro-machining process (with a nominal depth of 100 μm) show littleevidence of this border, and the terminal angle of the features isconsiderably narrower than the tertiary blade bevel.

This implies that there is significant elastic behavior occurring in themold material, as the tips of the mold cavities are narrowing by severaldegrees when the blade is retracted. This effect is observed for singlecavities as well as arrays of cavities.

To test the predictions of the semi-analytic model, the cutting forcesduring micro-machining were measured. A wax specimen of width 1 cm wasattached to a six-axis force/torque sensor (ATI Gamma SI-32-2.5) whichwas mounted in a CNC milling machine, and a variety of micro-machiningtrajectories were used to create cavities in the wax. The trajectorieswere linear and differed by trajectory angle, ranging from θ=36° to 60°,and maximum depth, ranging from t=20 μm to 100 μm. The blade centerlineangle was λ=60° in all cases, an angle found empirically to producefeatures with the desired directional behavior. In this exemplaryexperiment, the cavities were spaced far apart (0.5 mm tip-to-tip) sothat the interaction between them was negligible. The blade was widerthan the wax specimen so that its corners were not in contact.

The resulting force data were analyzed to find the cutting force Fcorresponding to the endpoint of each trajectory, the point in time whenthe tool was at its maximum cutting depth t for each cavity. The finalcavity shape, preserved by casting PDMS into the specimen, serves as arecord of the shape of the cavity at that same point in time. As shownin FIG. 7 a, these castings clearly show the triangular shape of thebuilt-up material adjacent to the leading side of the tool (consistentwith the model). By constructing a line from the tip of the cavity tothe front edge of the built-up region, and taking into account the widthof the wax specimen, it is possible to measure the area of the shearplane A and the shear plane angle φ (FIG. 7 a).

For each cavity, the value of F was projected onto the shear plane usingEq. 4 to produce an estimate of the shear stress f_(s)/A. Thisassumption is only accurate if there is no contact between the trailingside of the tool and the wax. If there is such contact, the measuredcutting force will be the sum of forces at the leading and trailing toolfaces, which cannot be separated using external measurements.

The measured values of f_(s)/A versus θ are plotted in FIG. 7 b, as wellas the shear yield stress of the wax k, calculated using both the Trescaand von Mises shear yield criteria, derived from the compressive yieldstress, which was determined through axial compression testing.

Even though the cutting depth varied from t=20 μm to 100 μm for eachtrajectory, causing some variance in the data, the trend is the same forall values of t. For trajectories near θ=λ=60°, there is substantialdisagreement between the measurements of f_(s)/A and the value of k,using either the Tresca or von Mises yield criteria. The direction ofthe cutting force F is nearly antiparallel to the shear plane, causingf_(s) to be negative instead of positive. This may be due to contactforces on the trailing side of the tool because, for trajectories θ>43°,it is expected that the secondary or tertiary bevels will contact thewax on the trailing side, due to the blade geometry.

For trajectories θ<43°, it is expected that there is no contact on thetrailing side of the tool and therefore the measured value of f_(s)/Ashould be equal to k in accordance with Eq. 5. Indeed, the data for theshallowest trajectory, θ=36°, are in agreement with Eq. 5. However, thedata for θ=42° are not. This disagreement cannot be explained completelyby the geometry of the blade. In this case, it is likely that contact isoccurring on the trailing side of the blade. This may be due to elasticrecovery of the wax (which was assumed negligible in the model) or itmay be that the tribological interaction between the tool, lubricant,and mold surface is more complicated than can be described in thissimple model.

In summary, the evidence appears to invalidate the assumption that thematerial on the trailing side of the tool is rigid, for the majority ofthe micro-machining trajectories tested. Theoretical modeling hasprovided useful qualitative insight into the micro-machining process,but the models considered here are unable to explain the actual cuttingforces, and they cannot necessarily be used to predict the deformationof the mold material in a process that involves multiple cavities beingformed in series. These realizations prompted an empirical investigationof the micro-machining process.

Predicting the cutting force is not strictly necessary to produce auseful adhesive mold insofar as the forces are small enough not todamage or significantly deflect the micro-machining tool. However, it isimportant to ascertain the effect of the micro-machining trajectory onthe shape of the mold cavities. To accomplish this, a characterizationexperiment was performed in which the trajectory angle was varied (againfrom θ=36° to 60°) while the nominal depth and tip-to-tip spacing of thecavities were kept constant at 100 μm and 60 μm respectively. At thisdepth and spacing, the cavity shapes were expected to be significantlyinfluenced by neighboring cavities, so a series of ten cavities was madefor each trajectory.

PDMS was cast into the mold cavities and the resulting adhesive sampleswere cut in cross-section and measured with a microscope, as shown inFIGS. 8 a-8 d. Ten cavities appear to be sufficient to attain asteady-state shape; the boundary conditions are different for theinitial cavity, but this only affects the first three cavities or fewer.In addition, the final cavity is sometimes a different shape from theprevious ones. In these cases, the final cavity shows the shape of anincipient cavity before it has been deformed to its completed shape bythe cavity following it. The 4th-9th cavities are representative of thecompleted shapes that would be created in a large adhesive array.

The height and angular width of the cavities change with the trajectoryangle due to several concurrent effects. For values of θ near 36°, thefeature height is significantly less than the nominal height of 100 μmbecause the cavities intersect one another below the original moldsurface (FIG. 8 a). As θ increases past 46°, there is an increasinglylarge difference in height between the incipient feature and thecompleted features (FIG. 8 b), indicating that permanent deformation onthe trailing side of the tool is occurring. The feature height reaches amaximum at θ=56°, where the trailing-side deformation causes the edgesof the cavities to be raised up above the original mold surface (FIG. 8c). As θ is increased further to θ=λ=60°, the features become shorteragain and the tip angle diminishes well below the angular width of theblade, indicating that the rearward deformation is causing the cavitiesto close up at their tips (FIG. 8 d). These trends are plotted in FIG.9.

Samples of micromachined adhesives were fabricated to test theiradhesive properties. The blade was held at θ=60° and the trajectory waschosen to be θ=48°, an angle approximately parallel to the rear face ofthe tool, and found empirically to push most of the displaced materialforward. The nominal depth and tip-to-tip spacing were 100 μm and 60 μm.According to one aspect of the invention, the resulting cast syntheticadhesive can have wedge-shaped ridges with a tip-to-tip spacing as lowas 6 μm.

Adhesion force data were collected on an instrumented stage capable ofmoving the adhesive samples in and out of contact with a flat glasssubstrate along a specified trajectory and loading the adhesive in boththe normal and shear directions. The stage (Velmex MAXY4009W2-S4 andMA2506B-S2.5) is capable of 10 μm positioning resolution in the sheardirection and 1 μm in the normal direction. The adhesive samples weremounted on a stationary six-axis force/torque transducer (ATI GammaSI-32-2.5) with a force measurement resolution of approximately ±10 mN.The transducer is mounted on a two-axis goniometer to allow the adhesiveand substrate to be precisely aligned.

A sample of adhesive is tested by bringing it into contact with thesubstrate along a 45° approach trajectory until the adhesive reaches acertain preload depth. The preload depth is defined as the distance bywhich the adhesive is pressed into the substrate, measured normal to thesubstrate, from the position where the tips of the adhesive featuresmake first contact. Once the sample is at the appropriate preload depth,it is pulled out of contact along a trajectory at a specified pull-offangle. Such tests are referred to as load-pull tests. To obtain theadhesion limit curve, a battery of load-pull tests were performed forpreload depths ranging from 30-80 μm and pull-off angles ranging from0-90°.

Limit curves were generated for a 1.21 cm² patch of micro-machinedadhesive both before and after the post-treatment process step. Forcomparison, a limit curve was generated for a 0.37 cm² patch ofphotolithographic micro-wedge adhesive, having a rectangular pattern ofright triangular prisms (not lamellar ridges), approximately 20 μm wide,80 μm tall, 200 μm long, and with a tip-to-tip spacing of 40 μm betweenfeatures. These features are pictured in FIGS. 1 a-1 b.

The limit curves show the adhesives' performance in force space. Eachpoint corresponds to a combination of normal force and shear force atwhich failure occurred. The region above the curve is the “safe region”:Forces above the curve can be sustained by the adhesive; forces belowthe curve cause it to fail. The adhesive test results are consistentwith the directional adhesion model for geckos, in which adhesionincreases with increasing shear force.

As shown in FIG. 10, the photolithographic adhesive produces a maximumadhesive stress of approximately 18 kPa when loaded with a shear stressof approximately 51 kPa, and the micro-machined adhesive with nopost-treatment achieves a maximum adhesion of 13 kPa at a shear stressof 37 kPa. After post-treatment, the micro-machined adhesive has amaximum adhesion of 38 kPa at a shear stress of 49 kPa.

At high levels of shear stress, all of the adhesive samples show a“roll-off” in adhesion as increasing numbers of features start to slidealong the surface.

The micro-machining process has several advantages over thephotolithographic process, including increased yield, greater controlover the feature shape, a wider choice of mold materials, and vastlyimproved mold turnaround time (a matter of hours instead of weeks). Onedrawback is that the wax mold may become damaged when the PDMS isextracted from it, and cannot then be used a second time. To make moreadhesives, the top layer of the mold is removed and the underlyingmaterial is micromachined anew. However, the manufacturing flexibilityof micromachined adhesives makes up for this drawback, and they are aparticularly attractive option for applications when rapid designiteration is required.

The theoretical model above provides qualitative insight into themechanics of the micro-machining process and of the effects of varyingthe tool and approach angles when trying to make closely spacedcavities. However, its force predictions were not substantiated byexperimental results. This suggests that a more sophisticated model, forexample using large strain finite element modeling, is necessary foraccurate predictions.

Empirical evidence shows that a variety of shapes may be created bychanging the trajectory angle θ, including shapes which do not match theprofile of the micro-machining tool. Variations with the bladecenterline angle λ and with curved trajectories are possible.Different-shaped features affected by post-treatment are possible. Thepost-treatment process has a dramatic effect on the micro-machinedadhesive's performance: the maximum adhesion increases by nearly afactor of 3. The increase in adhesion is due to the better surfacefinish obtained on the contacting surfaces of the adhesive features(FIG. 5 c). According to an aspect of the invention, the tips of thewedge-shaped features include a film of cured elastomeric materialhaving a desired smoothness or texture on one or both sides, in order totake advantage of this increase in adhesion.

The post-treated micro-machined adhesive also achieves more than twicethe maximum adhesion obtained previously with photolithographic wedges.For practical reasons, it is difficult to make the photolithographicwedges at the same angle of inclination as the micro-machined wedges;instead, they have one vertical and one angled surface. Consequently,they are stiffer in the normal direction and produce a larger elasticforce that subtracts from the net adhesive force. The micro-machiningprocess affords more freedom to vary the angle of inclination and taper,which affect the available adhesion at various levels of applied shearforce.

As a further illustration of the effects of varying wedge shape andorientation, the data in FIG. 10 also show much greater adhesion forpost-treated micro-machined wedges at low levels of applied shear. As aconsequence, the post-treated micro-machined adhesive can support amaximum loading angle of 80° away from the surface for light loads.Whether post-treated or not, the micro-machined adhesives arecontrollable because they have the property of frictional adhesion: theadhesion increases as the shear load increases, and the adhesion goes tozero as the shear load is removed because the limit curve goes throughthe origin. This property makes it possible for a climbing robot todetach its feet with very little effort, simply by removing the appliedshear force. The result is smooth, efficient climbing.

In addition to climbing, potential applications for gecko-inspireddirectional adhesives range from fumble-free football gloves tomanufacturing processes involving the handling of materials.

By following the process according to the embodiments of the invention,it is possible to create relatively large patches of gecko-inspireddirectional adhesives using inexpensive equipment. The wedgemicro-machining process also permits greater freedom to control theshapes of the features than is possible with molds produced byphotolithography. In the present case, by creating features with twoangled surfaces instead of one vertical and one angled surface, andutilizing a simple post-treatment “inking” process, it is possible toobtain a much higher maximum loading angle at low levels of shearloading. This could be useful for applications involving lightweightrobots such as micro air vehicles or for handling delicate materials.

Two requirements of the process described here are (1) a suitable moldmaterial with near-rigid/plastic behavior and (2) the ability to controlthe trajectory of the tool, thereby controlling the movement ofdisplaced material, so that mold cavities can be spaced close togetherwhile simultaneously controlling the cavity shape. The micro-machiningprocess does not yet match the smooth surface finish obtained withphotolithographic methods, but the addition of a post-treatment step canprovide a very smooth contacting face and allows more than double themaximum adhesion obtained with corresponding adhesives fromphotolithographic molds on a flat glass substrate.

The current invention uses inexpensive and readily available materials,including a computer-controlled stage with at least two degrees offreedom (e.g., a CNC milling machine), a microtome blade for the cuttingtool, blocks of wax for the molds, and dish soap for the lubricant. Manyembodiments are clearly possible. The indenting trajectory may bemodified to create different shaped features, with higher aspect ratios,narrower tips, or different angles. Preliminary experiments suggest thateven with the present tool and a suitable lubricant, it may be possibleto cut directly into a soft metal. The resulting mold would be much moredurable and could survive many molding cycles. Other possibilitiesinclude machining a temperature-hardening material such as polymer clay,or using an investment casting process to create a second-generationmold from a more durable material than wax.

The adhesives perform very well on glass, but do not perform as well onrougher surfaces. To improve the adhesion on everyday surfaces withmicro-scale roughness, a siping step could be employed after de-moldingthe adhesive. Specifically, the features could be cut perpendicular totheir longest dimension at a desired frequency (see FIG. 5 b), therebyallowing small, independent sections of the feature to conform tosurface roughness.

Additionally, with suitably precise and stiff positioning equipment,much smaller terminal features should also be possible. Even morecomplicated cavity geometries could be generated using a machiningapparatus with a rotational degree of freedom (allowing the tool tochange its angle during cutting), or by using a custom-shapedmicro-machining tool or multiple tools in sequence. Such a process couldcreate a hierarchical structure, with nano-features on the surfaces oflarger micro-wedges. Such developments could lead to a gecko-inspireddirectional adhesive that performs well on rough surfaces, a goal thathas thus far remained elusive.

The present invention has now been described in accordance with severalexemplary embodiments, which are intended to be illustrative in allaspects, rather than restrictive. Thus, the present invention is capableof many variations in detailed implementation, which may be derived fromthe description contained herein by a person of ordinary skill in theart. All such variations are considered to be within the scope andspirit of the present invention as defined by the following claims andtheir legal equivalents.

1. A method of forming synthetic dry adhesives, comprising: a. using awedge-shaped tool to form mold cavities in a mold, wherein said moldcavities comprise a depth t and a spacing h; b. filling said moldcavities with an elastomeric adhesive; c. removing said elastomericadhesive from said mold, wherein a tapered lamellar ridge extends from asurface of said elastomeric adhesive; d. treating a tip of saidextending tapered lamellar ridge with a film of uncured elastomericmaterial; and e. curing said film of uncured material while saidextending tapered lamellar ridge is pressed against a substrate surface.2. The method according to claim 1, wherein said mold comprises ahomogeneous wax composition having a Young's modulus to yield stressratio E/Y greater than
 100. 3. The method according to claim 1, whereinsaid wedge-shaped tool comprises at least a primary bevel.
 4. The methodaccording to claim 1, wherein said wedge-shaped tool comprises a primarybevel, a secondary bevel and a tertiary bevel.
 5. The method accordingto claim 1, wherein said wedge-shaped tool comprises a lubricatedsurface.
 6. The method according to claim 1, wherein said wedge-shapedtool is moved along a 2-dimensional or 3-dimensional trajectory intosaid mold until a tip of said wedge-shaped tool reaches said depth tbelow a top surface of said mold.
 7. The method according to claim 1,wherein a trajectory of said tool is controlled to move displaced moldmaterial in a desired direction, wherein said mold cavities aredesirably spaced and a shape of said cavities is controlled.
 8. Themethod according to claim 1, wherein a centerline of said wedge-shapedtool is set at an angle λ with respect to a top surface of said mold,wherein a trajectory of said tool is at an intermediate angle θ withrespect to a top surface of said mold, wherein said angle θ is in arange of 0<θ<λ.
 9. The method according to claim 1, wherein saidelastomeric adhesive comprises an elastomer selected from the groupconsisting of silicones, polyurethanes, and polypropylene.
 10. Themethod according to claim 1, wherein treating a tip of said extendingtapered lamellar ridge with a film of uncured elastomeric materialcomprises said uncured elastomeric material disposed on one or bothsides of said lamellar ridge.
 11. The method according to claim 1,wherein said substrate surface comprises a smooth or textured surface,wherein said surface is disposed to transfer a desired smoothness ordesired texture to a film of said uncured elastomeric material as saiduncured elastomeric material cures.
 12. The method according to claim 1,wherein a siping step is used when said adhesive is de-molded, whereinsaid siping step comprises a cut perpendicular to said extending taperedlamellar ridge at a desired frequency to improve adhesion on texturedsurfaces having micro-scale roughness, wherein independent adhesivesections of said extending tapered lamellar ridge conform to saidtextured surface.
 13. A synthetic dry adhesive, comprising: a. aclose-packed array of elastomeric adhesive wedge-shaped lamellar ridges,wherein a cross section of said close-packed array comprises a base of aleading edge of one said lamellar ridge contacting a base of a trailingedge of an adjacent said lamellar ridge, wherein said lamellar ridgecomprises an internal taper spanning from a base of said lamellar ridgeto a pointed tip of said lamellar ridge, wherein a centerline of saidlamellar ridge is angled relative to a direction normal to saidsynthetic dry adhesive; and b. a secondary elastomeric adhesive layerdisposed on one or both sides of said wedge-shaped lamellar ridge,wherein said secondary layer comprises a textured or flat surface. 14.The synthetic dry adhesive of claim 13, wherein said wedge-shapedlamellar ridge bends into a curve when it contacts a surface, whereuponthe radius of curvature of said wedge-shaped lamellar ridge increasesmonotonically with increasing shear load.
 15. The synthetic dry adhesiveof claim 13, wherein the tip-to-tip spacing between adjacent saidlamellar ridges is as low as 6 μm.
 16. The synthetic dry adhesive ofclaim 13, wherein said angle of said centerline of said lamellar ridgeis up to 50 degrees relative to said normal direction.
 17. The syntheticdry adhesive of claim 13, wherein both sides of said lamellar ridge isangled relative to said normal direction.
 18. The method according toclaim 13, wherein said elastomeric adhesive comprises an elastomerselected from the group consisting of silicones, polyurethanes, andpolypropylene.
 19. The synthetic dry adhesive of claim 13, wherein saidtip of said wedge-shaped lamellar ridge comprises a film of curedelastomeric material having a desired smoothness or texture on one orboth sides of said wedge-shaped lamellar ridge.
 20. The synthetic dryadhesive of claim 14, wherein said lamellar ridge comprises siping,wherein said siping is disposed across said wedge-shape lamellar ridge.